ELEKTRONIKA IR ELEKTROTECHNIKA,ISSN 1392-1215,VOL.19,NO.10,2013
1Abs ac —In his pape , a new compac ol age-mode ou -
phase oscilla o employing single z-copy ol age di e encing
ansconduc ance ampli ie (ZC-VDTA) and only g ounded
passi e elemen s is in oduced. The use o only g ounded
capaci o s and esis o s makes he p oposed ci cui ideal o
in eg a ed ci cui implemen a ion. The condi ion o oscilla ion
and he equency o oscilla ion a e independen ly adjus able.
The passi e and ac i e sensi i i ies o he p oposed ci cui
con igu a ion a e low. Expe imen al measu emen esul s using
eadily a ailable Maxim In eg a ed ICs MAX435 a e gi en o
p o e he heo y.
Index Te ms—Analog signal p ocessing, ou -phase
oscilla o , ol age-mode, z-copy ol age di e encing
ansconduc ance ampli ie , ZC-VDTA.
I. INTRODUCTION
Sinusoidal oscilla o s a e linea elec ic ci cui s ha a e
used in wide a ea o elec onics and ep esen an impo an
uni in many adio ecei e s, elecommunica ion,
ins umen a ion, con ol and da a moni o ing sys ems [1]–
[3]. Recen ly he ol age-mode (VM) ou -phase oscilla o s,
which a e special ype o mul iphase oscilla o s, ha e
ecei ed conside able a en ion in he li e a u e [4]–[13]. In
Table I he a ailable ci cui s a e lis ed and compa ed based
on ele an c i e ions. The gi en su ey shows ha hese
oscilla o s uc u es a e based on ope a ional ampli ie s (Op-
Amps) [4], [7], di e en ial di e ence cu en con eyo s
(DDCCs) [5], second-gene a ion cu en con eyo s (CCIIs)
[6], [8], [9], di e en ial ou pu -cu en in e e bu e ed
ampli ie (DO-CIBA) [10], ol age di e encing in e ing
bu e ed ampli ie s (VDIBAs) [12], o dual-ou pu
con olled gain cu en ollowe bu e ed ampli ie s (DO-
Manusc ip ecei ed Janua y 30, 2013; accep ed May 21, 2013.
Ing. No be He encsa , Ph.D. was suppo ed by he p ojec CZ.1.07/
2.3.00/30.0039 o B no Uni e si y o Technology. Resea ch desc ibed in
his pape was also in pa suppo ed by he p ojec SIX
CZ.1.05/2.1.00/03.0072 om he ope a ional p og am Resea ch and
De elopmen o Inno a ion, by he p ojec WICOMT
CZ.1.07/2.3.00/20.0007 inanced om he ope a ional p og am Educa ion
o compe i i eness, and Czech Science Founda ion p ojec s unde No.
P102/11/P489 and P102/09/1681.
CG-CFBAs) and cu en ampli ie (CA) [13]. In addi ion,
he Complemen a y Me al–Oxide–Semiconduc o (CMOS)-
RC based oscilla o s a e ecen ly also popula [11].
Conside ing he numbe o ac i e elemen s in abo e
men ioned VM ou -phase oscilla o s i can be seen ha a
leas wo ac i e building blocks (ABBs) a e equi ed o
hei ealiza ion. Howe e , ou de ailed s udy showed ha
used ABBs in [10] and [12] ep esen an in e connec ion o
wo sub-ci cui s such as cu en in e e and di e en ial
ou pu bu e ed ampli ie in case o [10] o ope a ional
ansconduc ance ampli ie (OTA) [14] and uni y-gain
in e ing ol age bu e in [12]. I should be also men ioned
ha in [5] and [7] addi ional ol age ollowe s/in e e s a e
needed. Hence, in hese ci cui s excessi e numbe o ABBs
is used. F om he monoli hic in eg a ion poin o iew,
ci cui s ha employ only g ounded passi e elemen s a e
a ac i e. Only ci cui s in [6], [8], and [9] sa is y his c ucial
c i e ion. Howe e , he oscilla o in [8] employs one
addi ional capaci o (in o al h ee) ha signi ican ly
inc eases he chip a ea in case o in eg a ion.
In 2008, se o new ABB concep s ha e been in oduced
[14] om hem ecen ly p obably he ol age di e encing
ansconduc ance ampli ie (VDTA) ecei ed he mos o
a en ion [15]–[19]. The VDTA belongs o new g oup o
ABBs so-called ‘ ol age di e encing’ elemen s and i is a
‘ ol age’ coun e pa o he well-know cu en di e encing
ansconduc ance ampli ie (CDTA) [14].
In his pape , o inc ease he uni e sali y o he
con en ional VDTA, he “z-cu en copy” echnique is wi h
ad an age used, which was p e iously in oduced o o he
ci cui concep s [14]. In [15]–[19] VDTA-based VM and
cu en -mode (CM) second- and ou -o de il e s, lossless
g ounded & loa ing induc ance simula o s, and CM
quad a u e oscilla o s we e published. Based on CM concep
om [19], his pape p esen s he i s VM ou -phase
quad a u e oscilla o using VDTA in he li e a u e and i s
p ac ical ealiza ion including ampli ude gain con ol (AGC)
ci cui . The p oposed ci cui employs only single z-copy
VDTA. Hence, he numbe o ABBs agains [4]–[13] is
educed. Mo eo e , i employs only g ounded capaci o s and
New Compac VM Fou -Phase Oscilla o
Employing Only Single Z-Copy VDTA and All
G ounded Passi e Elemen s
N. He encsa 1, R. So ne 2, J. Ko on1, J. Misu ec1, K. V ba1
1Depa men o Telecommunica ions, B no Uni e si y o Technology,
Technicka 12, 616 00 B no, Czech Republic
2Depa men o Radio Elec onics, B no Uni e si y o Technology,
Technicka 12, 616 00 B no, Czech Republic
[email p o ec ed]z
h p://dx.doi.o g/10.5755/j01.eee.19.10.5900
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ELEKTRONIKA IR ELEKTROTECHNIKA,ISSN 1392-1215,VOL.19,NO.10,2013
esis o s ha make he ci cui ideal o in eg a ed ci cui
implemen a ion. Expe imen al measu emen esul s on
equency o oscilla ion equal o 4 MHz wi h sa is ac o y
o al ha monic dis o ion a e included o suppo he heo y.
TABLE I. COMPARATIVE STUDY WITH PREVIOUSLY REPORTED VM FOUR-PHASE OSCILLATORS.
Re .
ABB ype
No. o ABBs
No. o g ounded R / C
No. o loa ing R / C
Resul s
0(Hz)
THD (%)
[4]
Op-Amp
4
0 / 2
10 / 0
measu emen s
22.89 k
< 0.1
[5]
DDCC
4b
2 / 2
2 / 0
simula ions
500 k
–
[6]
CCII
3
6 / 2
0 / 0
simula ions
10 k
–
[7]
Op-Amp
5b
0 / 1
3 / 1
simula ions
10 k
–
[8]
CCII
3
5 / 3
0 / 0
simula ions
1 M
–
[9]
CCII
2
5 / 2
0 / 0
simula ions
1 M
–
[10]
DO-CIBA
2
0 / 2
3 / 0
measu emen s
1 M
0.07
[11]
–a
–
0 / 0
4 / 2
simula ions
160.2 k
< 2.5
[12]
VDIBA
2
1 / 1
0 / 1
simula ions
8.5 M
< 2.25
[13]
DO-CG-CFBA+CA
3
0 / 2
3 / 0
simul. / meas.
978 k / 2.5 M
< 1 / < 0.6
P op.
ZC-VDTA
1
3 / 2
0 / 0
measu emen s
4 M
0.4 – 3.1
No es:
– No men ioned o no applicable;
aCMOS-RC ci cui ; bRe . [5] includes one ol age in e e and one ol age ollowe , [7] includes wo ol age in e e s and wo ol age ollowe s.
(a)
(b)
Fig. 1. (a) Ci cui symbol and (b) beha io al model o ZC-VDTA.
II. CIRCUIT DESCRIPTION
The ci cui symbol and beha io al model o ZC-VDTA
a e shown in Fig. 1(a) and Fig. 1(b), espec i ely. The ZC-
VDTA essen ially consis s o wo balanced-ou pu OTAs,
whe ein he di e ence o inpu ol ages V +and V –is
ans e ed by he i s ansconduc ance gain gm1 o cu en
a he e minals zand zc– (nega i e o z) and he ol age
d op a he e minal zis ans e ed o cu en a he
e minals x+ and x– (nega i e o x+) by second
ansconduc ance gain gm2. In p ac ice bo h
ansconduc ances gm1,2 can be simul aneously elec onically
con olled by ei he ex e nal DC bias cu en s o ol ages.
All six e minals exhibi high-impedance alues. Using
s anda d no a ion, he e minals ela ionship o an ideal ZC-
VDTA can be cha ac e ized by he ollowing hyb id ma ix
1 1
1 1
2
2
0
0.
0 0
0 0
z m m
zc m m
x m
z
x m
I g g V
I g g V
I g V
I g





     
   
 
   
 
     
     

   
(1)
The p oposed ealiza ion o VM ou -phase oscilla o
employing single ZC-VDTA, wo capaci o s, and h ee
esis o s, all in g ounded o m, is shown in Fig. 2. Using (1),
ou ine ci cui analysis yields he ollowing cha ac e is ic
equa ion (CE).
Fig. 2. P oposed VM ou -phase oscilla o .
Fig. 3. Model o he ZC-VDTA including pa asi ic elemen s.
 
21 2 1 2 1 1 1 2 1
CE : 1 0.
m m m
s C C R sC g R g g R   
(2)
F om (2) he condi ion o oscilla ion (CO) and he
equency o oscilla ion (FO) can be e alua ed as:
1 1
CO : 1,
m
g R 
(3)
1 2
0
1 2
1
FO : .
2
m m
g g
C C


(4)
F om (3) and (4) i is clea ha he CO can be con olled
independen ly o FO by means o a ying he esis o R1and
he FO can be adjus ed by he ansconduc ance gm2,
espec i ely. Thus, he p oposed oscilla o is an SRCO and
p o ides independen con ol o he CO and he FO.
III. NON-IDEAL ANALYSIS
Fo a comple e analysis, i is impo an o ake in o
accoun pa asi ics o ac i e elemen shown in Fig. 3:
Iz=

1gm1Vd,Izc–= –

2gm1Vd,Ix+=

1gm2Vz,Ix–= –

2gm2Vz, whe e Vd= (V +–V –),

iand

i ep esen
ansconduc ance gains o he ZC-VDTA ha di e om
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hei ideal alues by ansconduc ance acking e o s

1i
and

2i(|

1i|, |

2i| « 1), whe e i= 1, 2.
The pa asi ic esis ances R +,R –and pa asi ic
capaci ances C +,C –appea be ween he high-impedance
+ and – inpu e minals o he ZC-VDTA and g ound,
espec i ely, and hei ypical alues in case o ZC-VDTA
implemen a ion by Maxim In eg a ed ICs MAX435 a e
800 kǁ 5 pF.
The pa asi ic esis ances Rz,Rzc–and pa asi ic
capaci ances Cz,Czc–appea be ween he high-impedance z
and zc– auxilia y e minals o he ZC-VDTA and g ound,
espec i ely, and hei ypical alues a e
3.48 kǁ 10 pF and 3.5 kǁ 5 pF, espec i ely.
The pa asi ic esis ances Rx+,Rx–and pa asi ic
capaci ances Cx+,Cx–appea be ween he high-impedance
x+ and x– ou pu e minals o he ZC-VDTA and g ound,
espec i ely, and hei ypical alues a e 3.5 kǁ 5 pF.
Conside ing he e ec o a o emen ioned non-ideali ies on
he p oposed oscilla o shown in Fig. 2, he ollowing use ul
analysis can be p o ided:
A he node 1 he pa asi ic esis ances R +,Rzand
capaci ances C +,Cza e abso bed in o ex e nal esis o R1
and capaci o C1, espec i ely, as hey appea in shun wi h
hem and in analysis below hey a e labeled as R1and C1.
A he node 2 he pa asi ic capaci ances C –and Cx+a e
abso bed in o ex e nal capaci o C2as i appea s in shun
wi h hem and in u he analysis i is labeled as C2.
Fu he mo e, i mus be also men ioned ha in he same
node he pa asi ic esis ances R –and Rx+a e also in shun
and in u he analysis labeled as R x.
A nodes 3, 4 he pa asi ic esis ances Rzc–,Rx–a e
abso bed in o ex e nal esis o s R2and R3, espec i ely, as
hey appea in shun wi h hem and labeled as R2and R3.
Thus, he non-ideal e ec s o pa asi ic impedance a 1s ,
3 d, and 4 h nodes o he p oposed oscilla o a e educed, i
no comple ely elimina ed. A he node 2 he pa asi ic
capaci ance can also be abso bed in he ex e nal capaci o ,
bu he p esence o pa asi ic esis ance R x a his node
would change he ype o he impedance, which should be o
a pu ely capaci i e cha ac e . A possible solu ion is o make
he ope a ing equency 0> 1/(2

R xC2). Taking in o
accoun he a o emen ioned non-ideali ies, excep o he
pa asi ic capaci ances Czc–and Cx–, he CE in (2) becomes

21 2 1 1 1 2 1 2 1 1
1 1 1 1 2 1 1 1
CE :
1 0,
x x x m
x m m m
s C C R R s C R C R C R R g
R R g g R g

  
       
   
 
   
(5)
which by neglec ing he pa asi ic esis ance R x u ns o a
o m

21 2 1 2 1 1 1
1 1 1 1 2
CE : 1
0,
m
m m
s C C R sC R g
R g g

 
    
   

 
(6)
ha only by non-ideal ansconduc ance gains

1and

1
di e s om he ideal CE in (2) and subsequen ly om he
ideal CO and FO in (3) and (4). Hence, in p ac ice a p ecise
design o he ZC-VDTA should be conside ed o alle ia e
he non-ideal e ec s.
IV. MEASUREMENT RESULTS
In o de o con i m he heo e ical s udy, he beha io o
he p oposed VM ou -phase oscilla o has been e i ied by
expe imen al measu emen s. The comple e ci cui
con igu a ion o he p oposed oscilla o supplemen ed by
AGC ci cui including speci ic alues o passi e elemen s is
shown in Fig. 4. In measu emen s he ZC-VDTA was
implemen ed using comme cially a ailable ICs MAX435 by
Maxim In eg a ed. The DC powe supply ol ages we e
equal o ±5 V. Gene a ed ol ages in all nodes a e a ailable
h ough addi ional ol age bu e s. Fo his pu pose
ope a ional ampli ie LT1364 was used. The AGC ci cui
con ains cascade diode double and BS250 FET ansis o .
Expe imen al measu emen s we e ca ied ou using
RIGOL DS1204B ou -channel oscilloscope and HP4395A
ne wo k-spec um analyze . The spec um analyze equi es
impedance ma ching (50 ). The e o e, he ol age bu e s
LT1364 ha e been e y impo an .
Measu emen esul s a e shown in Fig. 5–Fig. 7. Figu e 5
shows all ou ansien esponses oge he . Expe imen ally
measu ed oscilla ion equency was 04 MHz, which
ma ches well wi h heo y. The equency spec um o Vo2is
depic ed in Fig. 6.
Fig. 4. Comple e ci cui con igu a ion used o expe imen al es .
Fig. 5. Measu emen esul s: ansien esponses a all ou ou pu s
(Vo1- blue colo , Vo2- ed colo , Vo3- g een colo , Vo4- o ange colo ).
THD alue ob ained om measu emen s o ou pu
ampli udes Vo2a 04 MHz was 0.58 %. Tunabili y o 0
ia gm2and ou pu ol age le els and THD s. 0du ing he
uning p ocess a e shown in Fig. 7. Ideal equency ange o
FO uning was calcula ed om 2.18 o 14.49 MHz.
Howe e , his calcula ion does no ake in o accoun he
main eal ea u es o ac i e elemen s used. The e o e,
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ELEKTRONIKA IR ELEKTROTECHNIKA,ISSN 1392-1215,VOL.19,NO.10,2013
expec ed ange o FO = {1.65 – 11} MHz was ob ained by
mo e accu a e calcula ion, which includes mainly pa asi ic
capaci ances and low alues o esis ance in high-impedance
nodes (ou pu s o MAX435).
Fig. 6. F equency spec um o Vo2.
1
10
0.4
20
1
10
20
0 (MHz)
gm2 (mA/V)
Ideal
Calcula ed
Measu ed
(a)
1
10
0
0.5
1.0
1.5
2.0
2.5
0
1
2
3
4
5
Ou pu ol age (Vp-p)
THD (%)
0 (MHz)
Vo1,3
Vo2,4
THD_Vo1,3
THD_Vo2,4
(b)
Fig. 7. (a) Tunabili y o 0 ia gm2, (b) ou pu ol age le els and THD s. 0
du ing he uning p ocess.
Measu ed equency ange co esponds wi h expec ed
calcula ions, since FO was in ange om 1.36 MHz–
10 MHz. Adjus men o FO was ealized by changes o
ansconduc ance gm2 om 0.4 mA/V o 18.3 mA/V. Fo
Vo1,3 ou pu ampli udes eached alues om 0.5 V o 1 V
and o Vo2,4 om 1.1 V o 2.2 V, espec i ely. THD alues
luc ua e be ween 0.4 %–1.4 % and 2.3 %–3.1 % o ou pu s
Vo1,3 and Vo2,4, espec i ely. In addi ion, he ampli ude o
Vo1,3 a e almos unchangeable in ange om 1.36 MHz o
7 MHz. In o e all, ob ained esul s ma ch e y well wi h
heo y.
V. CONCLUSIONS
This pape p esen ed a new compac ol age-mode ou -
phase oscilla o employing ecen ly in oduced single
z-copy ol age di e encing ansconduc ance ampli ie and
only g ounded passi e elemen s. The use o only g ounded
capaci o s and esis o s makes he p oposed ci cui ideal o
in eg a ed ci cui implemen a ion. The condi ion o
oscilla ion and he equency o oscilla ion a e independen ly
adjus able. Expe imen al esul s using comme cially
a ailable in eg a ed ci cui s con i m he easibili y o he
p oposed ci cui .
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